I don't believe I've ever heard a name for such quantities. Integer multiples of a number are all integers, so integer fractions of a number would also be all integers, which doesn't make sense to me at all unless you are talking only about the cases where the division works out to an integer, for example, 12/4. What you have with A/2, A/3, etc. is fractions which have integers as a divisors, but whether that's a useful mathematical concept is up to the mathematicians to decide.

In mathematics, you usually use mathematical jargon, which is largely symbolic, rather than narrative English. So if A is any kind of number, then you'd typically say: "nA (or A/n), where n is an integer." So for nA, you have: A, 2A, 3A, ..., and for n/A, you have A, A/2, A/3, ....